Question

If $n$ is a positive integer divisible by $2,5$ and $7$, which of the following is true?
$I.n^2+100$ is divisible by $100$
$II.n+18$ is divisible by $14$
$III.n^2+1$ is divisible by $2$

• A. $I$ and $II$ only
• B. $I,II$ and $III$
• C. $I$ only
• D. $I$ and $III$ only
• E. $II$ and $III$ only

Answer 1

Answer: (C)

$I$ only

$n$ is divisible by $2,5,7.$

Let $n=70$

Hence $n^2+100=4000+100=5000$

Which is divisible by $100.$

Hence $\left(i\right)$ is correct$.$

$n+18=70+18=88,$ which is not divisible by $14.$

$n^2+1=4900+1=4901,$ which is not divisible by $2.$

Hence only $1$ is correct$.$